Selling to strategic and loss‐averse consumers: Stocking,procurement, and product design policies

Motivated by the presence of loss‐averse decision making behavior in practice, this article considers a supply chain consisting of a firm and strategic consumers who possess an S‐shaped loss‐averse utility function. In the model, consumers decide the purchase timing and the firm chooses the inventory level. We find that the loss‐averse consumers' strategic purchasing behavior is determined by their perceived gain and loss from strategic purchase delay, and the given rationing risk. Thus, the firm that is cognizant of this property tailors its inventory stocking policy based on the consumers' loss‐averse behavior such as their perceived values of gain and loss, and their sensitivity to them. We also demonstrate that the firm's equilibrium inventory stocking policy reflects both the economic logic of the traditional newsvendor inventory model, and the loss‐averse behavior of consumers. The equilibrium order quantity is significantly different from those derived from models that assume that the consumers are risk neutral and homogeneous in their valuations. We show that the firm that ignores strategic consumer's loss‐aversion behavior tends to keep an unnecessarily high inventory level that leads to excessive leftovers. Our numerical experiments further reveal that in some extreme cases the firm that ignores strategic consumer's loss‐aversion behavior generates almost 92% more leftovers than the firm that possesses consumers’ loss‐aversion information and takes it into account when making managerial decisions. To mitigate the consumer's forward‐looking behavior, we propose the adoption of the practice of agile supply chain management, which possesses the following attributes: (i) procuring inventory after observing real‐time demand information, (ii) enhanced design (which maintains the current production mix but improves the product performance to a higher level), and (iii) customized design (which maintains the current performance level but increases the variety of the current production line to meet consumers’ specific demands). We show that such a practice can induce the consumer to make early purchases by increasing their rationing risk, increasing the product value, or diversifying the product line. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 435–453, 2015     

Single machine parallel batch scheduling subject to precedence constraints

We consider the single machine parallel batch scheduling problems to minimize makespan and total completion time, respectively, under precedence relations. The complexities of these two problems are reported as open in the literature. In this paper, we settle these open questions by showing that both problems are strongly NP‐hard, even when the precedence relations are chains. When the processing times of jobs are directly agreeable or inversely agreeable with the precedence relations, there is an O(n²) time algorithm to minimize the makespan. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Machine scheduling with an availability constraint and job delivery coordination

In this paper we study the scheduling problem that considers both production and job delivery at the same time with machine availability considerations. Only one vehicle is available to deliver jobs in a fixed transportation time to a distribution center. The vehicle can load at most K jobs as a delivery batch in one shipment due to the vehicle capacity constraint. The objective is to minimize the arrival time of the last delivery batch to the distribution center. Since machines may not always be available over the production period in real life due to preventive maintenance, we incorporate machine availability into the models. Three scenarios of the problem are studied. For the problem in which the jobs are processed on a single machine and the jobs interrupted by the unavailable machine interval are resumable, we provide a polynomial algorithm to solve the problem optimally. For the problem in which the jobs are processed on a single machine and the interrupted jobs are nonresumable, we first show that the problem is NP‐hard. We then propose a heuristic with a worst‐case error bound of 1/2 and show that the bound is tight. For the problem in which the jobs are processed on either one of two parallel machines, where only one machine has an unavailable interval and the interrupted jobs are resumable, we propose a heuristic with a worst‐case error bound of 2/3. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Rectilinear m-Center problem

In this article we consider the unweighted m-center problem with rectilinear distance. We preent an O(n^m–2 log n) algorithm for the m-center problem where m ≥ 4.     

Two-characteristic markov-type manpower flow models

A two-dimensional state space Markov Model of a Manpower System with special structure is analyzed. Examples are given from the military services. The probabilistic properties are discussed in detail with emphasis on computation. The basic equations of manpower stocks and flows are analyzed.     

The payment scheduling problem

Large complicated projects with interdependent activities can be described by project networks. Arcs represent activities, nodes represent events, and the network's structure defines the relation between activities and events. A schedule associates an occurrence time with each event: the project can be scheduled in several different ways. We assume that a known amount of cash changes hands at each event. Given any schedule the present value of all cash transactions can be calculated. The payment scheduling problem looks for a schedule that maximizes the present value of all transactions. This problem was first introduced by Russell [2]; it is a nonlinear program with linear constraints and a nonconcave objective. This paper demonstrates that the payment scheduling problem can be transformed into an equivalent linear program. The linear program has the structure of a weighted distribution problem and an efficient procedure is presented for its solution. The algorithm requires the solution of triangular systems of equations with all matrix coefficients equal to ± or 0.     

Optimal policies for a multi-echelon inventory system with demand forecasts

Consider an inventory system consisting of two installations, the stocking point and the field. Each period two decisions must be made: how much to order from outside the system and how much to ship to the field. The first decision is made based on the total amounts of stock then at the two installations. Next a forecast of the demand in the current period is sent from the field to the stocking point. Based upon a knowledge of the joint distribution of the forecast and the true demand, and the amounts of stock at the two installations, a decision to ship a certain amount of stock to the field is taken. The goal is to make these two decisions so as to minimize the total n-period cost for the system. Following the factorization idea of Clark and Scarf (1960), the optimal n period ordering and shipping policy, taking into account the accuracy of the demand forecasts, can be derived so as to make the calculation comparable to those required by two single installations.     

Hit probability for a chain-like series of shots—a simple formula

To find the hit probability for a series of correlated shots is, with conventional methods, a very tedious job even for the simplest statistical distributions. Experimental data, however, commonly show the shots lying chain-like on smooth curves about the target. For this case this paper introduces a new method of finding the hit probability without the use of correlation coefficients. The method is based on a transformation, where the target is transformed into a point and each bullet into an area the size of the target.     

Approximations for the consolidation of multiechelon repair facilities

This paper develops and illustrates an approximate approach for analytically assessing the impacts on both costs and service of consolidation of repair facilities. The repair facilities are two echelon generalizations of the classical repairmen problem in which two types of failures, say major and minor, can occur, each type requiring repair at a different echelon: The questions addressed are the reductions possible in spares, repairmen, and service rates due to the consolidated system's increased efficiency, as well as the physical separation between the users and the consolidated repair facility that is economical. The method of analysis is based upon asymptotic approximations developed for the repairmen problem, valid when the number of operational equipments is large (greater than 50); it is helpful since it provides a tractable means for predicting the steady-state performance of the decentralized and consolidated installations as a function of the many parameters involved without having to resort to an exhaustive computation of all the exact steady-state probabilities.